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5x^2-109x=50
We move all terms to the left:
5x^2-109x-(50)=0
a = 5; b = -109; c = -50;
Δ = b2-4ac
Δ = -1092-4·5·(-50)
Δ = 12881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-\sqrt{12881}}{2*5}=\frac{109-\sqrt{12881}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+\sqrt{12881}}{2*5}=\frac{109+\sqrt{12881}}{10} $
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